WASHINGTON — Massachusetts Democrats in Congress are digging in against cuts to benefit programs as part of any deal to avert an impending fiscal crisis, reflecting the difficult calculus facing President Obama as he negotiates with Republicans.

Members of the Bay State’s House delegation — all Democrats — said they are wrestling with conflicting impulses. They want to avoid the blow to the economy that would result from hitting the so-called “fiscal cliff,” the spending cuts and tax hikes that automatically kick in at year’s end if lawmakers cannot come up with a better plan.

But they said in interviews this week that they are unwilling to support cuts to Social Security, Medicare, and Medicaid that would erode these safety-net benefits, which the Democratic Party has defended for decades. Representative James P. McGovern of Worcester said Obama and Democrats are facing a “moment of truth’’ in the next few weeks that will test the party’s commitment to core principles.

“I want Democrats to act like Democrats,’’ he said.

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While much of Washington’s attention has been focused on Republican opposition to raising the tax rates for the wealthy, Democrats’ opposition to cutting benefit programs looms equally large. To win passage of any House deal, leaders will need to cobble together a broad coalition, and Democratic defections could scuttle any pact.

McGovern and other Democrats are opposing such proposals as raising the eligibility age for Medicare from 65 to 67 or slashing Medicaid spending. They also reject a plan to link Social Security benefits to a more conservative inflation index, which is expected to slightly reduce annual increases. All of these concepts are being entertained to varying degrees on Capitol Hill and had been reported to be under consideration by Obama at various points during his first term.

Democrats also are increasingly concerned about a rush to a deal. Private talks between administration officials and congressional leaders, McGovern said, might produce an 11th-hour pact before Jan. 1 that harms the elderly and the poor in ways that have not been fully discussed in public hearings.

“I’m worried,’’ said McGovern. “Even if it’s a bad deal, the pressure on Democrats to cave will be enormous.’’

Massachusetts Democrats are especially adamant that Social Security not be touched, because it is not contributing to the deficit and the Social Security trust fund is projected to be solvent through 2033.

Cuts to Social Security “would not go down well,’’ said Representative Richard E. Neal of Springfield, a member of the tax-writing Ways and Means Committee. “I would say to the president: Hold your nerve. Hold your nerve and keep negotiating.’’

The Democrats’ opposition to benefit cuts, combined with Republican hostility to tax rate increases, has created the sense in Washington this week that a quick deal may be more elusive than Obama and congressional leaders signaled after Obama’s reelection two weeks ago.

Treasury Secretary Timothy Geithner went to Capitol Hill Thursday to offer Republicans a plan with tax increases of $1.6 trillion over a decade and various cuts that included $400 billion in health and retirement programs but did not achieve any breakthroughs. In fact, the opposite appeared true.

“Despite the claims that the president supports a balanced approach, the Democrats have yet to get serious about real spending cuts,” House Speaker John A. Boehner said Thursday as he announced “no substantive progress’’ in the talks.

Democrats and Republicans alike profess to seek long-term changes in Medicare that would improve its economic health. Current projections say it will be insolvent, without changes, by 2024. But some Democrats say there are a range of changes and reforms to save money that stop short of raising the eligibility age, such as money-saving tweaks promoting homecare and coordinated care and cracking down on fraud.

Massachusetts Democrats said they did not want to be rushed into accepting major entitlement cuts that, in their view, would not help the economy and would only harm the middle class.

Although the delegation was united on a hands-off approach to Social Security, some differences emerged surrounding the more critical problem of how to preserve Medicare. Representative Edward J. Markey of Malden, the longest-serving of the Massachusetts delegation, opposes raising the Medicare age of eligibility. Representative Michael E. Capuano of Somerville, however, said he is open to raising the age as long as the eventual deal raises tax rates on the wealthy.

Neal said he would consider raising the eligibility age of Medicare by one month a year. He said cracking down harder on fraud in Medicare could save $60 billion a year in savings.

Each lawmaker interviewed was willing to consider higher Medicare premium payments for the wealthy and other such “means-testing’’ options.

Democrats contend they have the upper hand in negotiations, a position they believe will only get stronger if no deal is reached before the end of the year. If tax cuts for all Americans are allowed to expire at midnight on Dec. 31, as scheduled, then Democrats would quickly introduce legislation to restore the cuts for 98 percent of the people and leave out the wealthy. Republicans would face intense pressure to pass such legislation.

Democrats are hopeful that even the threat of that scenario will force Republicans to accept a “baby grand bargain” on taxes before year’s end, while delaying consideration of changes to entitlement benefit programs until 2013, Markey said.

“I don’t want to go off the cliff, but I don’t want a deal at the expense of the middle class,’’ he said.

Senator John Kerry did not respond directly when asked for his view on entitlements but said in an e-mailed statement that “Republicans have to get serious about revenues and get precise. I’ve heard a lot of vague talk about closing loopholes, but I want to see what loopholes they’re talking about and what revenues they’re talking about.’’

Adding to the Democrats’ sense of strength is a belief that the fiscal cliff is actually a “fiscal slope.’’ The impact of extracting an estimated $500 billion from the economy — in the form of expiring tax cuts and automatic “sequestration’’ spending cuts agreed to in 2011 — would not come all at once; rather, it would be spread over the course of 2013. There would still be time to act to repair the damage in the early part of the year, although a message of continued gridlock could roil markets sooner.

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